EP0372058B1 - Method and apparatus for determining the position and velocity of a target in inertial space - Google Patents
Method and apparatus for determining the position and velocity of a target in inertial space Download PDFInfo
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- EP0372058B1 EP0372058B1 EP89906615A EP89906615A EP0372058B1 EP 0372058 B1 EP0372058 B1 EP 0372058B1 EP 89906615 A EP89906615 A EP 89906615A EP 89906615 A EP89906615 A EP 89906615A EP 0372058 B1 EP0372058 B1 EP 0372058B1
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- 230000001133 acceleration Effects 0.000 claims abstract description 25
- 238000005259 measurement Methods 0.000 abstract description 34
- 238000004364 calculation method Methods 0.000 description 16
- 239000013598 vector Substances 0.000 description 12
- 238000010586 diagram Methods 0.000 description 4
- 230000010354 integration Effects 0.000 description 4
- 230000003534 oscillatory effect Effects 0.000 description 3
- 230000000694 effects Effects 0.000 description 2
- 238000006467 substitution reaction Methods 0.000 description 2
- NCGICGYLBXGBGN-UHFFFAOYSA-N 3-morpholin-4-yl-1-oxa-3-azonia-2-azanidacyclopent-3-en-5-imine;hydrochloride Chemical compound Cl.[N-]1OC(=N)C=[N+]1N1CCOCC1 NCGICGYLBXGBGN-UHFFFAOYSA-N 0.000 description 1
- 230000001154 acute effect Effects 0.000 description 1
- 150000001875 compounds Chemical class 0.000 description 1
- 230000007123 defense Effects 0.000 description 1
- 238000013213 extrapolation Methods 0.000 description 1
- 230000000977 initiatory effect Effects 0.000 description 1
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- 230000000737 periodic effect Effects 0.000 description 1
- 230000000644 propagated effect Effects 0.000 description 1
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- C—CHEMISTRY; METALLURGY
- C12—BIOCHEMISTRY; BEER; SPIRITS; WINE; VINEGAR; MICROBIOLOGY; ENZYMOLOGY; MUTATION OR GENETIC ENGINEERING
- C12Q—MEASURING OR TESTING PROCESSES INVOLVING ENZYMES, NUCLEIC ACIDS OR MICROORGANISMS; COMPOSITIONS OR TEST PAPERS THEREFOR; PROCESSES OF PREPARING SUCH COMPOSITIONS; CONDITION-RESPONSIVE CONTROL IN MICROBIOLOGICAL OR ENZYMOLOGICAL PROCESSES
- C12Q1/00—Measuring or testing processes involving enzymes, nucleic acids or microorganisms; Compositions therefor; Processes of preparing such compositions
- C12Q1/02—Measuring or testing processes involving enzymes, nucleic acids or microorganisms; Compositions therefor; Processes of preparing such compositions involving viable microorganisms
- C12Q1/24—Methods of sampling, or inoculating or spreading a sample; Methods of physically isolating an intact microorganisms
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/66—Radar-tracking systems; Analogous systems
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- C—CHEMISTRY; METALLURGY
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- C12N5/00—Undifferentiated human, animal or plant cells, e.g. cell lines; Tissues; Cultivation or maintenance thereof; Culture media therefor
- C12N5/06—Animal cells or tissues; Human cells or tissues
Definitions
- the present invention relates to a method and a system for determining the position and velocity of a target in inertial space.
- this known system In order to maintain an accurate track file on the target, this known system must receive data at regular intervals relating to the target's position and movement. Unfortunately, for a number of reasons, such information may not always be available on a continuous basis. When the flow of tracking data is intermittent or otherwise interrupted, the a.m. conventional tracking system has not been able to measure all the parameters necessary to determine a target cue (range, range rate, and aspect angle, for example) and therefore has heretofore simply operated on the basis that the target must be within some "uncertainty zone". This problem becomes particularly acute when such data is unavailable for extended periods of time.
- the conventional system typically assumes a worst case target maneuver which results in excessively large uncertainty zones. This leads to data losses and excessively long target search times. This, in turn, compounds target discrimination and association problems with obviously undesirable consequences for commercial and military applications. Further, multi-parameter searches, (i.e., for range, range rate, and possibly angle) for initial target acquisition and minimum system complexity, dictate that the uncertainty bounds be minimized within the constraints of possible target maneuver.
- the present invention is a method and associated system for developing and maintaining a cue on an airborne target, i.e., target position and velocity in inertial space.
- the invention is based on the following assumptions: 1) that a complete set of target parameters, indicating target position and velocity in inertial space, is available as a minimum during some initial time period; 2) that the target scalar velocity is essentially constant throughout flight and that there are no significant longitudinal accelerations; 3) that the worst case target lateral acceleration (in quadrature to the instantaneous target velocity vector) is known over some period of time; 4) that the velocity and attitude parameters of the tracking platform are of known accuracy; 5) an estimate of the accuracy of all target measurement parameters is available; 6) the system tracking function maintains the antenna line-of-sight coincident with the line-of-sight from the platform to the target when angle measurements are available and extrapolates the position when measurements are not available; and 7) during any period in which no target data is available, the target performs a worst case maneuver with regard to uncertainty.
- a key step in the method of the present invention is in the use of all available measurement data to estimate the target scalar velocity, V T and aspect angle ⁇ cue at the time of measurement. That is, in accordance with the teachings of the present invention, if the target velocity V T and the target aspect angle ⁇ cue are known, and there is a momentary loss of tracking data, then given that when the target accelerates, it changes aspect angle ⁇ cue (which is particularly true for airborne targets), ⁇ cue can be recalculated. And since the target scalar velocity V T is assumed to be constant, a new target cue may be provided with a minimal uncertainty zone.
- the teachings of the present invention are provided below in three sections. First, it is disclosed how the target velocity V T and aspect angle ⁇ cue are calculated based on the above assumptions and a steady flow of tracking data. Next, the methodology for the determination of the position of the target is provided with respect to range rate and aspect angle estimates or bounds (minimums and maximums) using an "accelerating target model" and the assumption that the target makes a maximum (worst case) maneuver during a period of unavailability of tracking data. Finally, the range rate uncertainty due to inaccuracies in the measurement of target and platform range rates is determined and combined with the acceleration model range rate parameters to determine the overall range rate interval containing the target. The platform and target range rate uncertainty contributions are also integrated separately to determine range uncertainty and then combined with the accelerating target range parameters to determine the overall (global) range interval.
- Fig. 1 is a vectorial representation of the position and movement of a non-maneuvering target at point T relative to a platform at point P.
- the inertial frame chosen for computation is aligned with the line-of-sight (LOS) between the platform and the target being the X axis, the Y axis being positive to the right (normal to the X axis and into the page), and the Z axis being normal to the X axis and positive up (ANTENNA frame) since the antenna is assumed to be tracking the designated target.
- V T is a vector representing the velocity of the target in antenna coordinates.
- V TXA R' PT + V PXA [1]
- V TYA R PT * ⁇ ' AZ + V PYA [2]
- V TZA R PT * ⁇ ' EL + V PZA [3]
- V T (V TXA 2 + V TYA 2 + V TZA 2) 1/2 [4]
- R PT is the range between the target and the platform
- R' PT is the range rate
- ⁇ ' AZ is the azimuth component of the line-of-sight rate ⁇ '
- ⁇ ' EL is the elevation component of same.
- Fig. 2 shows a functional block diagram 10 of the method of the present invention.
- target velocity data is available target velocity V T and aspect angle ⁇ cue may be calculated in accordance with equations 4 and 5 above.
- range R PT , range rate R' PT and line-of-sight angular rate ⁇ ' are input along with target velocity V TA and platform velocity V PA to calculate target velocity V T and aspect angle ⁇ cue in inertial space.
- the radar tracking antenna will rotate at the line-of-sight rate such that the angle ⁇ will be zero.
- the angle ⁇ represents the pointing error of the tracking system.
- the accelerating target model 14 of Fig. 2 serves to provide range, range rate and angle uncertainty bounds R PTa(max) , R PTa(min) , R' PTa(max) , R' PTa(min) , ⁇ max and ⁇ min respectively due to unknown target accelerations.
- the computations are performed given prior target velocity V T and aspect angle ⁇ cue , a prior estimate of range R PT , maximum target acceleration A Tmax , and the platform velocity vector V PA .
- Range and range rate estimates are provided by the midpoint of the range and range rate bounds. As shown below, range and range rate estimates yield target velocity and aspect angle estimates with smaller bounds than those afforded by prior techniques.
- the present invention proceeds along the path 38 corresponding to 'no target velocity data' from the decision point 34.
- the method of the present invention ascertains whether valid LOS rate measurement data ⁇ ' is available at decision point 42. If so, in branch 44, at 48, the invention calculates the azimuth and elevational components ⁇ ' AZ and ⁇ ' EL respectively of the LOS rate ⁇ ' from the target track. These values are then used with the range R PT and the platform velocity values to provide the target velocity components V TYA and V TZA in accordance with equations [2] and [3] above respectively.
- V Tc 2 V TYA 2 + V TZA 2 .
- R' PT valid range rate data
- V TXA X-axis component of the velocity vector V TXA using equation [1] above.
- the velocity vector V TXA is then combined with V Tc to provide a new target velocity estimate V T .
- the new target velocity estimate V T is then used to compute ⁇ cue using equation [5]. If there is no valid range rate measurement data at 50, then ⁇ cue is calculated based on the previous value of V T .
- the method of the present invention checks for valid range rate data. If valid range rate data is available, at step 66, it is used to calculate a new X-axis target velocity component, in accordance with equation [1]. This component is then used to calculate ⁇ cue in accordance with equation [5]. If no valid range rate data is available, the system extrapolates new velocity and aspect angle calculations based on previous values. In a tracking radar capable of multi-parameter target measurements, (range, range rate, angle), a certain precedence is implied.
- Angle measurements may be obtained to control the seeker line-of-sight and derive line-of-sight rate estimates for broadcasting targets; e.g., ECM sources; in the absence of range and/or range rate measurements.
- targets e.g., ECM sources
- range and range rate measurements on the target are typically accompanied by angle data. Otherwise, it would be difficult to confirm that the source of the measurements is the desired target.
- blocks 60 and 66 may consequently be eliminated from the flow chart of Fig. 3.
- the target velocity is represented by vectors V T(min) and V T(max) and the target has aspect angles of ⁇ min and ⁇ max respectively.
- ⁇ min ⁇ cue - ⁇ '*(delta T) [7]
- ⁇ max ⁇ cue + ⁇ '*(delta T) [8]
- ⁇ ' the aspect rate
- delta T the relevant time interval. Since the polarity of the target acceleration is unknown, the range rate computations below are performed for both possible polarities of ⁇ '*(delta T), that is, both the minimum and the maximum target aspects.
- the vectors V T(min) and V T(max) represent excursions from the initial aspect angle ⁇ cue of ⁇ '*(delta T) in the negative and positive directions ⁇ min and ⁇ max respectively.
- the vectors V T(min) and V T(max) represent the maximum possible excursions of the target during the period of data interruption.
- the vectors V T(min) and V T(max) have line-of-sight components of V TXA(min) and V TXA(max) respectively.
- Fig. 4 illustrates the track geometry under constant target acceleration conditions if the maneuver is computation allowed to continue.
- Equations [12] and [13] below facilitate the calculation of the range R.
- R' c can be calculated as the midpoint in the range provided by using equation [11] for the assumed unknown target maneuver, and for the same maneuver, R' L can be calculated as the midpoint in the range provided by using equation [9]
- R' c can be accumulated or integrated to provide R c and R' L can be accumulated from the original R to provide R L and since the range R supplied at the outset provides a normalization factor to provide an initial range rate R i , the total range R may be acquired by integrating equation [13]. (The total range thus acquired accounts for the down range (LOS) and cross range components.) Use of the minimum range rate value provides the minimum range while the maximum range value provides the maximum range.
- Fig. 4 shows exemplary track geometries under constant target acceleration.
- a target which is assumed to maintain a positive lateral acceleration will have an oscillatory trajectory 200 similar to that shown below the LOS, while a target which is assumed to maintain a negative lateral acceleration will have an oscillatory trajectory 202 similar to that shown above the LOS.
- the method of the present invention for resolving this ambiguity is to propagate ⁇ '*(delta T) , letting it grow until the slope of R' changes. This is illustrated in Fig. 5.
- Fig. 6 shows a flow chart 300 of an illustrative routine by which iterative calculations of the range and range rate parameters are performed to determine the assumed maneuver acceleration termination (aspect rotation limiting) point by the accelerating target model 14.
- the aspect rotation limiting feature of the present invention is illustrated for minimum and maximum range in a geometric sense although the actual limiting is based on the range rate parameters; i.e., minimum range rate propagates to minimum range and maximum range rate propagates to maximum range.
- the accumulated values of ⁇ '*(delta T) are then used in accordance with equation [7] and [8] above to provide ⁇ min and ⁇ max . (Separate criteria for ⁇ min and ⁇ max .)
- Fig. 7 shows a flow chart 400 of an illustrative routine by which the LOS angle error ⁇ limits are calculated for the assumed maneuvering target including lateral acceleration termination (aspect rotation limiting) by the accelerating target model 14.
- ⁇ min and ⁇ max are given as follows.
- the values of ⁇ min and ⁇ max are set to ⁇ cue whenever ⁇ cue is calculated regardless of the type of measurement used in the calculation. At this time, the minimum and maximum values of R' are also equal since the ⁇ cue calculation is an estimate of the integral of the unknown target maneuver. However, since the actual target maneuver history is unknown, the range estimate is only updated when a range measurement is input. For this condition, the values of R PTA(min) and R PTA(max) are set to the measurement value.
- the above calculations presume that the measurement data is perfect.
- the present invention provides a technique for incorporating uncertainties due to inaccuracies in the measured parameters.
- ⁇ RPT ( ⁇ RP 2 + ⁇ RT 2) 1/2 [15]
- the range uncertainty ⁇ R is combined with the accelerating target model range bounds R PTa(max) and R PTa(min) at block 18 to provide the range uncertainty interval R PT(min) and R PT(max) .
- the average of these values R PT(min) and R PT(max) provides the best estimate of range R PT .
- the method for controlling (resetting) the range rate uncertainty inputs and the integrations thereof for each type of measurement is provided in the flow chart 70 of Fig. 8.
- valid data is available either from an external source along path 76 or from platform measurements via path 90, it is used to minimize uncertainty. That is, if live data is available, the uncertainty parameters are set in accordance with the validity of the live data.
- the target component of range rate uncertainty is set to the uncertainty in the derived target component along the line-of-sight.
- the platform component is set to the uncertainty in platform velocity along the line-of-sight (see block 82).
- target inertial position data is provided, the target component of range error is set to zero and the platform component of range uncertainty is set to the combination of the uncertainty in the target position along the line-of-sight and the uncertainty in the platform position along the line-of-sight (see block 88).
- the values of ⁇ 2 RT and ⁇ 2 R'T are a priori uncertainty estimates of the target parameters which may only be modified by subsequent external or live measurement data.
- the a priori estimate of the target component of range rate error ⁇ 2 R'T is propagated for the entire interval since the last valid range measurement to determine the target component of range error in block 96 via path 94.
- the platform component of range error is determined by integrating the platform range rate uncertainty over the interval since the last live data with an initial condition equal to its uncertainty at the time of the live data.
- the platform range rate uncertainty is calculated by integrating the platform acceleration uncertainty over the interval of no measurements with an initial condition equal to the platform range rate uncertainty at the time of the last live data in block 106 via path 104. In these calculations, delta T is the iteration time interval and N*(delta T) is the total interval since the last live data input.
- the range uncertainty parameters are set in accordance with the data validity in block 100 via path 98.
- the entire uncertainty in range is assigned to the platform parameter ⁇ 2 RP for computation convenience; and the target component ⁇ 2 RT and the interval parameter N are set to zero.
- live range rate data is available via path 108 from decision point 102, the range rate uncertainty parameters are reset in accordance with data validity.
- the platform component is set to zero and the entire measurement uncertainty is assigned to the target parameter, ⁇ 2 R'T .
- the range and range rate uncertainty parameters are adjusted in accordance with the use of this data in the computation of target aspect (block 12 of Fig. 2).
- the error in the range rate component derived from line-of-sight rate data is determined in block 116 and assigned to the target component. Since line-of-sight rate data may be derived when range and range rate measurements are not available, its use in determining the instantaneous target range rate component does not allow reset of the platform components of range and range rate uncertainties. Further, the target component of range error due to a priori target range rate uncertainty in the interval between measurements can not be eliminated by knowing the current target aspect since the target trajectory is unknown. Therefore, the target component of range uncertainty is added to the platform component and the measurement interval parameter is set to zero.
- ⁇ RPT is provided to the range uncertainty interval calculation routine 18 which computes the global minimum and maximum range:
- R PT(min) R PTa(min) - K * ⁇ RPT [16]
- R PT(max) R PTa(max) + K * ⁇ RPT [17]
- K is a scalar relating to the desired level of certainty in terms of the number of standard deviations ⁇ used in the calculation (normally three).
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Abstract
Description
- The present invention relates to a method and a system for determining the position and velocity of a target in inertial space.
- A method and a system of that kind are known from "Conference Proceedings of Military Electronic Defense Expo 1978", 3-5 October 1978, Interavia, (Geneva, CH), F.A. Faruqi, pages 414-432. In this known method resp. system the target is tracked and three orthogonal velocity components in inertial space are provided, wherein an aspect angle of the target relative to a line-of-sight to a platform is obtained as tracking data. Furthermore, an actual target maneuver is estimated by using these tracking data.
- In order to maintain an accurate track file on the target, this known system must receive data at regular intervals relating to the target's position and movement. Unfortunately, for a number of reasons, such information may not always be available on a continuous basis. When the flow of tracking data is intermittent or otherwise interrupted, the a.m. conventional tracking system has not been able to measure all the parameters necessary to determine a target cue (range, range rate, and aspect angle, for example) and therefore has heretofore simply operated on the basis that the target must be within some "uncertainty zone". This problem becomes particularly acute when such data is unavailable for extended periods of time.
- The conventional system typically assumes a worst case target maneuver which results in excessively large uncertainty zones. This leads to data losses and excessively long target search times. This, in turn, compounds target discrimination and association problems with obviously undesirable consequences for commercial and military applications. Further, multi-parameter searches, (i.e., for range, range rate, and possibly angle) for initial target acquisition and minimum system complexity, dictate that the uncertainty bounds be minimized within the constraints of possible target maneuver.
- Therefore, it is the object of the present invention to improve a method according to the preamble of
claim 1 and a system according to the preamble ofclaim 10 in such a way that the uncertainty zone resulting from an interruption in the availabilty of target tracking data is minimized. - According to the present invention, this object is solved by the advantageous measures indicated in the characterizing part of
claim - By these advantageous measures it is possible to minimize the uncertainty zone resulting from an interruption in the availabilty of target tracking data under all circumstances. Therefore, nearly no target discrimination and association problems exist.
- In the following, the invention will be described in more detail with reference to the accompanying drawings in which:
- Fig.1 is a vectorial representation of the position and movement of a target relative to a platform;
- Fig. 2 shows a functional block diagram of the method of the present invention;
- Fig. 3 is a flow chart illustrating the methodology of the present invention by which the target velocity and aspect are calculated;
- Fig. 4 is a vectorial representation of the position and movement of a target under constant acceleration relative to a platform;
- Fig. 5 shows target trajectories for minimum and maximum range predictions (target acceleration effects);
- Figs. 6(a) and 6(b) provide a flow chart of the methodology of the accelerating target model of the present invention, with aspect limiting, for the iterative calculation of range and range rate parameters;
- Figs. 7(a) and 7(b) provide a flow chart of the methodology of the accelerating target model of the present invention for calculating angle parameters, with aspect limiting; and
- Fig. 8 is a flow chart of the method for controlling the range and range rate uncertainty inputs and the integrations thereof for each type of measurement of the present invention.
- The present invention is a method and associated system for developing and maintaining a cue on an airborne target, i.e., target position and velocity in inertial space. The invention is based on the following assumptions: 1) that a complete set of target parameters, indicating target position and velocity in inertial space, is available as a minimum during some initial time period; 2) that the target scalar velocity is essentially constant throughout flight and that there are no significant longitudinal accelerations; 3) that the worst case target lateral acceleration (in quadrature to the instantaneous target velocity vector) is known over some period of time; 4) that the velocity and attitude parameters of the tracking platform are of known accuracy; 5) an estimate of the accuracy of all target measurement parameters is available; 6) the system tracking function maintains the antenna line-of-sight coincident with the line-of-sight from the platform to the target when angle measurements are available and extrapolates the position when measurements are not available; and 7) during any period in which no target data is available, the target performs a worst case maneuver with regard to uncertainty.
- A key step in the method of the present invention is in the use of all available measurement data to estimate the target scalar velocity, VT and aspect angle βcue at the time of measurement. That is, in accordance with the teachings of the present invention, if the target velocity VT and the target aspect angle βcue are known, and there is a momentary loss of tracking data, then given that when the target accelerates, it changes aspect angle βcue (which is particularly true for airborne targets), βcue can be recalculated. And since the target scalar velocity VT is assumed to be constant, a new target cue may be provided with a minimal uncertainty zone.
- The teachings of the present invention are provided below in three sections. First, it is disclosed how the target velocity VT and aspect angle βcue are calculated based on the above assumptions and a steady flow of tracking data. Next, the methodology for the determination of the position of the target is provided with respect to range rate and aspect angle estimates or bounds (minimums and maximums) using an "accelerating target model" and the assumption that the target makes a maximum (worst case) maneuver during a period of unavailability of tracking data. Finally, the range rate uncertainty due to inaccuracies in the measurement of target and platform range rates is determined and combined with the acceleration model range rate parameters to determine the overall range rate interval containing the target. The platform and target range rate uncertainty contributions are also integrated separately to determine range uncertainty and then combined with the accelerating target range parameters to determine the overall (global) range interval.
- Fig. 1 is a vectorial representation of the position and movement of a non-maneuvering target at point T relative to a platform at point P. The inertial frame chosen for computation is aligned with the line-of-sight (LOS) between the platform and the target being the X axis, the Y axis being positive to the right (normal to the X axis and into the page), and the Z axis being normal to the X axis and positive up (ANTENNA frame) since the antenna is assumed to be tracking the designated target. V T is a vector representing the velocity of the target in antenna coordinates. It has an initial measured aspect angle of βcue, a velocity component along the line-of-sight of VTXA, and a cross velocity component normal to the line-of-sight of
-
- Fig. 2 shows a functional block diagram 10 of the method of the present invention. When target velocity data is available target velocity VT and aspect angle βcue may be calculated in accordance with equations 4 and 5 above. In the functional block diagram of Fig. 2, range RPT, range rate R'PT and line-of-sight angular rate ϑ' are input along with target velocity V TA and platform velocity V PA to calculate target velocity VT and aspect angle βcue in inertial space.
- Fig. 3 is a flow chart illustrating the methodology of the present invention by which the target velocity and aspect are calculated. As shown in the
flow chart 30 of Fig. 3, the target velocity and aspect angle computations are performed at block 40 if some source of valid target velocity data is available. Given that the above measurement data was available at time T = 0, the position of the target at time T₁ can be extrapolated in accordance with the following equation:
where RPTXA'(T₁) is the relative velocity along the x axis of the antenna, and RPTcA'(T₁) is the cross component of same. Similarly, the inertial rotation of the line-of-sight ϑ to the target at time T₁ relative to that at time T₀ is defined as follows:
In the absence of target maneuver, the radar tracking antenna will rotate at the line-of-sight rate such that the angle ϑ will be zero. (Thus, the angle ϑ represents the pointing error of the tracking system.) This then represents the general case. However, as it can not be assumed that the target will not maneuver during a period the data unavailability, the accelerating target model below extrapolates the last valid data assuming a worst case target maneuver. - The accelerating
target model 14 of Fig. 2 serves to provide range, range rate and angle uncertainty bounds RPTa(max), RPTa(min), R'PTa(max), R'PTa(min), ϑmax and ϑmin respectively due to unknown target accelerations. The computations are performed given prior target velocity VT and aspect angle βcue, a prior estimate of range RPT, maximum target acceleration ATmax, and the platform velocity vector V PA . Range and range rate estimates are provided by the midpoint of the range and range rate bounds. As shown below, range and range rate estimates yield target velocity and aspect angle estimates with smaller bounds than those afforded by prior techniques. - Referring again to Fig. 3, if tracking data flow is interrupted the present invention proceeds along the
path 38 corresponding to 'no target velocity data' from thedecision point 34. Next, the method of the present invention ascertains whether valid LOS rate measurement data ϑ' is available atdecision point 42. If so, in branch 44, at 48, the invention calculates the azimuth and elevational components ϑ'AZ and ϑ'EL respectively of the LOS rate ϑ' from the target track. These values are then used with the range RPT and the platform velocity values to provide the target velocity components VTYA and VTZA in accordance with equations [2] and [3] above respectively. These values are then used to calculate VTc in accordance with a modified equation [4] above, viz.,decision point 50, if valid range rate data R'PT is available, it is used to calculate X-axis component of the velocity vector VTXA using equation [1] above. The velocity vector VTXA is then combined with VTc to provide a new target velocity estimate VT. The new target velocity estimate VT is then used to compute βcue using equation [5]. If there is no valid range rate measurement data at 50, then βcue is calculated based on the previous value of VT. - Returning to
decision point 42, if no LOS rate measurement data is available, then atpoint 60, the method of the present invention checks for valid range rate data. If valid range rate data is available, at step 66, it is used to calculate a new X-axis target velocity component, in accordance with equation [1]. This component is then used to calculate βcue in accordance with equation [5]. If no valid range rate data is available, the system extrapolates new velocity and aspect angle calculations based on previous values. In a tracking radar capable of multi-parameter target measurements, (range, range rate, angle), a certain precedence is implied. Angle measurements may be obtained to control the seeker line-of-sight and derive line-of-sight rate estimates for broadcasting targets; e.g., ECM sources; in the absence of range and/or range rate measurements. However, range and range rate measurements on the target are typically accompanied by angle data. Otherwise, it would be difficult to confirm that the source of the measurements is the desired target. In these systems, blocks 60 and 66 may consequently be eliminated from the flow chart of Fig. 3. - The target velocity and aspect angle values are used to provide range, range rate and pointing error outputs from the accelerating
target model 14. These values are calculated as follows. First, it is noted that if the target accelerates, it changes its aspect angle β generating an aspect angular rate β' given by:
where AT is the (lateral) acceleration of the target and AT(max) is the aircraft maneuver limit. This has the effect of changing the aspect angle of the target such that its velocity vector V T moves from point A to point B of Fig. 1 for maximum negative accelerations and to point C for maximum positive accelerations. At points B and C, the target velocity is represented by vectors V T(min) and V T(max) and the target has aspect angles of βmin and βmax respectively. Note that:
where β' is the aspect rate and delta T is the relevant time interval. Since the polarity of the target acceleration is unknown, the range rate computations below are performed for both possible polarities of β'*(delta T), that is, both the minimum and the maximum target aspects. - The vectors V T(min) and V T(max) represent excursions from the initial aspect angle βcue of β'*(delta T) in the negative and positive directions βmin and βmax respectively. The vectors V T(min) and V T(max) represent the maximum possible excursions of the target during the period of data interruption. The vectors V T(min) and V T(max) have line-of-sight components of VTXA(min) and VTXA(max) respectively. Fig. 4 illustrates the track geometry under constant target acceleration conditions if the maneuver is computation allowed to continue.
- The range rate R'L along the line-of-sight is defined as the difference between the velocity components along the line-of-sight of the target VTXA and the platform VPXA:
Substitution of the minimum and maximum values of the velocity components as provided above yields corresponding minimum and maximum values of the range rate along the line-of-sight R'L. Integration of the range rate R'L over the range defined by these minimum and maximum values thereof and addition of an initial range position Ro yields the minimum and maximum line-of-sight range values RL(min) and RL(max) respectively. - In Fig. 1 since the line-of-sight angular rate ϑ' is given by:
where R is the range, it can be seen that if the cross components VTc and VPc if the velocity vectors V T and V P respectively, are equal, the line-of-sight angular rate ϑ' is equal to 0 for - For this, it is necessary to know the value of the cross velocity term VTc because as the target maneuvers, there is a change in angle rate ϑ' of the line-of-sight and a change in range rate along the line-of-sight. The range rate across the line-of-sight R'c may be approximated by equation 11 below:
where
where
Which states that the new calculated range rate R'i+1 is equal to the product of the range rate across the LOS R'c times the previous range calculation across the LOS Rci plus the range rate along the LOS R'L times the previous range calculation along the LOS RLi all divided by the total range calculated for the previous iteration. Thus, for these aspect angles, since R'c can be calculated as the midpoint in the range provided by using equation [11] for the assumed unknown target maneuver, and for the same maneuver, R'L can be calculated as the midpoint in the range provided by using equation [9], R'c can be accumulated or integrated to provide Rc and R'L can be accumulated from the original R to provide RL and since the range R supplied at the outset provides a normalization factor to provide an initial range rate Ri, the total range R may be acquired by integrating equation [13]. (The total range thus acquired accounts for the down range (LOS) and cross range components.) Use of the minimum range rate value provides the minimum range while the maximum range value provides the maximum range. - If the extrapolation time interval is allowed to increase arbitrarily, the values of the R' parameters, will be oscillatory due to the periodic nature of the individual components. This is illustrated in Fig. 4 which shows exemplary track geometries under constant target acceleration. A target which is assumed to maintain a positive lateral acceleration will have an
oscillatory trajectory 200 similar to that shown below the LOS, while a target which is assumed to maintain a negative lateral acceleration will have anoscillatory trajectory 202 similar to that shown above the LOS. Obviously, this can create considerable ambiguity with respect to the target position and trajectory. The method of the present invention for resolving this ambiguity is to propagatesecond trajectory 202. Logic would be provided to terminate the maneuver whenever the slope of the range rate parameters change. This could easily be implemented by one of ordinary skill in the art. Fig. 6, for example, shows aflow chart 300 of an illustrative routine by which iterative calculations of the range and range rate parameters are performed to determine the assumed maneuver acceleration termination (aspect rotation limiting) point by the acceleratingtarget model 14. The aspect rotation limiting feature of the present invention is illustrated for minimum and maximum range in a geometric sense although the actual limiting is based on the range rate parameters; i.e., minimum range rate propagates to minimum range and maximum range rate propagates to maximum range. By this procedure, the absolute minimum and maximum values of range rate for a target initiating an unknown maneuver at t = 0 are calculated, and the integration of these range rates provides minimum and maximum values of range. The accumulated values of - A similar procedure is performed for the target pointing error values, insofar as the aspect calculation is concerned. The LOS angle error ϑ due to target maneuver is simply:
where RC and RL are provided above. This calculation is performed with continuous aspect rate until the value is maximized, at which time the maneuver is terminated. Fig. 7, shows aflow chart 400 of an illustrative routine by which the LOS angle error ϑ limits are calculated for the assumed maneuvering target including lateral acceleration termination (aspect rotation limiting) by the acceleratingtarget model 14. The values of ϑmin and ϑmax are given as follows.
and
The values of βmin and βmax are set to βcue whenever βcue is calculated regardless of the type of measurement used in the calculation. At this time, the minimum and maximum values of R' are also equal since the βcue calculation is an estimate of the integral of the unknown target maneuver. However, since the actual target maneuver history is unknown, the range estimate is only updated when a range measurement is input. For this condition, the values of RPTA(min) and RPTA(max) are set to the measurement value. - Thus, range, range rate and pointing error and aspect angle bounds for worst case target maneuver are provided.
- The above calculations presume that the measurement data is perfect. The present invention provides a technique for incorporating uncertainties due to inaccuracies in the measured parameters.
- In the absence of measurements of range and range rate parameters, separate calculations are performed to determine the target contribution to range rate uncertainty and the platform contribution to range rate uncertainty. These parameters are combined with the acceleration model range rate parameters to determine the overall range rate interval containing the designated target. The platform and target contributions are also integrated separately to determine range uncertainty and then combined with the accelerating target range parameters to determine the overall range interval. See the associated
blocks block 16 of Fig. 2.) In addition, the platform and target contributions to range rate uncertainty σ'RP and σ'RT are integrated, squared summed and square rooted atblock 24 to provide the target range uncertainty:
The range uncertainty σR is combined with the accelerating target model range bounds RPTa(max) and RPTa(min) atblock 18 to provide the range uncertainty interval RPT(min) and RPT(max). The average of these values RPT(min) and RPT(max) provides the best estimate of range RPT. - The method for controlling (resetting) the range rate uncertainty inputs and the integrations thereof for each type of measurement is provided in the flow chart 70 of Fig. 8. To the extent that valid data is available either from an external source along path 76 or from platform measurements via
path 90, it is used to minimize uncertainty. That is, if live data is available, the uncertainty parameters are set in accordance with the validity of the live data. Thus, atdecision point 78, when target velocity data is provided with an indication of its uncertainty, the target component of range rate uncertainty is set to the uncertainty in the derived target component along the line-of-sight. The platform component is set to the uncertainty in platform velocity along the line-of-sight (see block 82). Similarly, if atdecision point 84 target inertial position data is provided, the target component of range error is set to zero and the platform component of range uncertainty is set to the combination of the uncertainty in the target position along the line-of-sight and the uncertainty in the platform position along the line-of-sight (see block 88). The values of σ²RT and σ²R'T are a priori uncertainty estimates of the target parameters which may only be modified by subsequent external or live measurement data. - If no fresh data from any source is available, the a priori estimate of the target component of range rate error σ²R'T is propagated for the entire interval since the last valid range measurement to determine the target component of range error in
block 96 viapath 94. The platform component of range error is determined by integrating the platform range rate uncertainty over the interval since the last live data with an initial condition equal to its uncertainty at the time of the live data. The platform range rate uncertainty is calculated by integrating the platform acceleration uncertainty over the interval of no measurements with an initial condition equal to the platform range rate uncertainty at the time of the last live data inblock 106 viapath 104. In these calculations, delta T is the iteration time interval and - When a live range measurement is available, the range uncertainty parameters are set in accordance with the data validity in
block 100 viapath 98. The entire uncertainty in range is assigned to the platform parameter σ²RP for computation convenience; and the target component σ²RT and the interval parameter N are set to zero. When live range rate data is available viapath 108 fromdecision point 102, the range rate uncertainty parameters are reset in accordance with data validity. For computational convenience, the platform component is set to zero and the entire measurement uncertainty is assigned to the target parameter, σ²R'T. - When valid line-of-sight rate data is available at
decision point 112, the range and range rate uncertainty parameters are adjusted in accordance with the use of this data in the computation of target aspect (block 12 of Fig. 2). The error in the range rate component derived from line-of-sight rate data is determined in block 116 and assigned to the target component. Since line-of-sight rate data may be derived when range and range rate measurements are not available, its use in determining the instantaneous target range rate component does not allow reset of the platform components of range and range rate uncertainties. Further, the target component of range error due to a priori target range rate uncertainty in the interval between measurements can not be eliminated by knowing the current target aspect since the target trajectory is unknown. Therefore, the target component of range uncertainty is added to the platform component and the measurement interval parameter is set to zero. - Thus, in accordance with equation [15] above, σRPT is provided to the range uncertainty
interval calculation routine 18 which computes the global minimum and maximum range:
where the minimum and maximum platform to target range parameters for the 'no data' case are provided by the acceleratingmodel routine 14 and K is a scalar relating to the desired level of certainty in terms of the number of standard deviations σ used in the calculation (normally three). - Note that the platform errors in cross velocity and cross range components (the integral of cross velocity) are negligible in comparison to the corresponding target maneuver induced components and are therefore ignored in the computations of Fig. 8. It should also be noted that the flow chart of Fig. 8 is merely illustrative of the manner in which the computations may be performed to account for measurement error. Any specific implementation would depend on the system in which it is embedded.
Claims (10)
- A method for determining the position and velocity of a target (T) in inertial space, comprising the steps of[a] tracking the target (T) and providing three orthogonal velocity components (V TXA , V TYA , V TZA ) in inertial space and an aspect angle (β cue ) of the target (T) relative to a line-of-sight to a platform (P) as tracking data; and[b] estimating an actual target maneuver by using said tracking data;
characterized by the further steps of[c] computing the scalar velocity (V T ) of the target (T) in an inertial reference frame by providing the square root of the sum of the squares of said orthogonal velocity components (V TXA , V TYA , V TZA );[d] computing said aspect angle (β cue ) of the target (T) relative to said line-of-sight to the platform (P) as an inverse sinusoidal function of the ratio of one (V TXA ) of said orthogonal velocity components (V TXA , V TYA , V TZA ) and said scalar velocity (V T ), when said tracking data is available; and[e] estimating the actual target maneuver to develop a minimum uncertainty zone of said aspect angle (β cue ) of the target (T) by using a prior scalar velocity (V T ) and a prior aspect angle (β cue ) of the target (T) in combination with an assumed worst case lateral target acceleration, when said tracking data is not available. - The method of Claim 1, wherein said step [d] of computing said aspect angle (βcue) of the target (T) includes the step of computing an aspect angle (βcue) which is equal to the arccos of the ratio of said one velocity component (VTXA) of the target (T) to said scalar velocity (VT) of the target (T).
- The method of Claim 1 or 2, wherein said step [e] includes the steps of:[f] obtaining a measure of the range rate (R'PT) of the target (T) relative to said platform (P);[g] computing a new velocity component (VTXA) of the target (T) along said line-of-sight (VPXA) by adding said range rate (R'PT) to a velocity of said platform (P) along said line-of-sight (VPXA); and[h] computing a new aspect angle by means of the aspect angle (βcue) equal to the arccos of the ratio of said new velocity component (VTXA) of the target (T) to said scalar velocity (VT) of the target (T)
- The method of Claim 1, 2 or 3, wherein said step [e] includes the steps of:[f] obtaining a measure of the rate of change (ϑ') of the angle between the line-of-sight between the platform (P) and the target (T) and providing the azimuthal (ϑ'AZ) and elevational components (ϑ'EL) thereof;[g] computing a new velocity component of the target (T) along a Y axis (VTYA) by multiplying an estimate of the range RPT along the line-of-sight between the platform (P) and the target (T) by said azimuthal component (ϑ'AZ) and adding thereto any velocity of the platform (P) in along said Y axis (VTYA);[h] computing a new velocity component of the target (T) along a Z axis (VTZA) by multiplying an estimate of the range (RPT) along the line-of-sight between the platform (P) and the target (T) by said elevational component (ϑ'EL) and adding thereto any velocity of the platform (P) in along said Z axis (VTZA); and[i] computing a cross velocity (VTc) of the target (T) by taking the square root of the sum of the squares of said new velocity components along said Y and Z axes (VTYA and VTZA respectively).
- The method of Claim 4, wherein said step [e] includes the step of calculating a new aspect angle (βcue) equal to the arcsin of the ratio of said target cross velocity (VTc) to said scalar velocity (VT).
- The method of Claim 4, wherein said step [e] further includes the steps of:[j] obtaining a measure of the range rate (R') of the target (T) relative to the platform (P) along the line-of-sight;[k] computing a new velocity component (VTXA) of the target (T) along the line-of-sight by adding said range rate (R'PT) to any velocity of the platform (P) along the line-of-sight;[l] computing a new scalar velocity (VT) by taking the square root of the sum of the squares of the new velocity component (VTXA) of the target (T) along the line-of-sight and said cross velocity (VTc); and[m] computing a new aspect angle (βcue) equal to the arccos of the ratio of the the new velocity component (VTXA) of the target (T) along the line-of-sight to the new scalar velocity (VT).
- The method of one of Claims 1 to 6, including the step of bounding said aspect angle (βcue) by setting the minimum and maximum range rates of the target (T) at to the angles at which the range rate changes slope.
- The method of Claim 7, including the step of bounding said aspect angle (βcue) by setting the minimum and maximum range of the target (T) relative to the platform (P) by integrating said minimum and maximum range rates.
- The method of one of Claims 1 to 6, including the step of bounding said aspect angle (βcue) by maximizing the pointing error (ϑ) of the line-of-sight from the platform (P) to the target (T) equal to the arctan of the ratio of any cross range (RC) of the target (T) to the range of the target (T) along the line-of-sight.
- A system for determining the position and velocity of a target (T) in inertial space, including[a] means for tracking the target (T) and for providing three orthogonal velocity components (V TXA , V TYA , V TZA ) in inertial space and an aspect angle (β cue ) of the target (T) relative to a line-of-sight to a platform (P) as tracking data; and[b] estimating means (48) for estimating an actual target maneuver by using said tracking data;
characterized by :[c] means (40) for computing the scalar velocity (V T ) of the target (T) in an inertial reference frame by providing the square root of the sum of the squares of said orthogonal velocity components (V TXA , V TYA , V TXA ); and[d] means (40) for computing said aspect angle (β cue ) of the target (T) relative to said line-of-sight to the platform (P) as an inverse sinusoidal function of the ratio of one (V TXA ) of said orthogonal velocity components (V TXA , V TYA , V TZA ) and said scalar velocity (V T ), when said tracking data is available; wherein[e] said estimating means (48) is estimating the actual target maneuver to develop a minimum uncertainty zone of said aspect angle (β cue ) of the target (T) by using a prior scalar velocity (V T ) and a prior aspect angle (β cue ) of the target (T) in combination with an assumed worst case lateral target acceleration, when said tracking data is not available.
Applications Claiming Priority (2)
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US07/197,015 US4959800A (en) | 1988-05-20 | 1988-05-20 | Method and apparatus for determining the position and velocity of a target in inertial space |
US197015 | 1998-11-20 |
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EP0372058B1 true EP0372058B1 (en) | 1993-08-18 |
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JP2523369B2 (en) * | 1989-03-14 | 1996-08-07 | 国際電信電話株式会社 | Method and apparatus for detecting motion of moving image |
JP2736122B2 (en) * | 1989-07-14 | 1998-04-02 | 株式会社東芝 | Target position estimation device |
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US5325098A (en) * | 1993-06-01 | 1994-06-28 | The United States Of America As Represented By The Secretary Of The Navy | Interacting multiple bias model filter system for tracking maneuvering targets |
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USH1980H1 (en) | 1996-11-29 | 2001-08-07 | The United States Of America As Represented By The Secretary Of The Air Force | Adaptive matched augmented proportional navigation |
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1988
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ES2013501A6 (en) | 1990-05-01 |
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WO1989011662A1 (en) | 1989-11-30 |
AU3744589A (en) | 1989-12-12 |
KR900702379A (en) | 1990-12-06 |
JP2931348B2 (en) | 1999-08-09 |
TR25425A (en) | 1993-02-04 |
CA1333634C (en) | 1994-12-20 |
IL90126A (en) | 1993-01-14 |
NO900283D0 (en) | 1990-01-19 |
DE68908536T2 (en) | 1993-12-02 |
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DE68908536D1 (en) | 1993-09-23 |
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